Joel Matip’s fifth goal for the Reds, this a powerful header at the Kop end, edged the hosts ahead after a first half with promising chances for both sides.
And Jürgen Klopp’s team took further command soon after the interval as Mohamed Salah was fouled in the area and successfully dispatched the penalty.
Salah claimed the third with a sublime spin, sprint and strike before the hour – rendering Lucas Torreira’s late conversion a consolation for the Gunners.
The victory was Liverpool’s 12th in a row in the Premier League, equalling the club record set in 1990, and leaves the Reds as the only team with a 100 per cent record in the division.
Team news
Klopp made two changes to the XI that started at Southampton a week ago, with Fabinho and Jordan Henderson brought in for James Milner and Alex Oxlade-Chamberlain.
Liverpool: Adrian, Alexander-Arnold, Matip, Van Dijk, Robertson, Fabinho, Wijnaldum (Milner, 69), Henderson, Mane (Oxlade-Chamberlain, 77), Salah, Firmino (Lallana, 85).
Unused substitutes: Kelleher, Gomez, Shaqiri, Origi.
First half
Turned around to attack towards the Kop end in the first half, Liverpool wasted little time in going for a breakthrough – and came close within two minutes.
They stole possession around the halfway line and Matip quickly swept a pass out to the left for Andy Robertson to utilise the space open in front of him.
When he arrived at the edge of the box the left-back opted for a low cross-shot that was wide of the opposite post and just evaded the incoming run of Roberto Firmino.
The Reds were pressing Arsenal back to good effect but the visitors could, and perhaps should, have taken the lead themselves in the 11th minute.
Virgil van Dijk shepherded a long pass away from the threat of Nicolas Pepe and back towards Adrian but the goalkeeper’s attempted clearance only found Pierre-Emerick Aubameyang outside the area.
The Gunners striker tried to lift a finish up and over those between him and the exposed net but sent the ball the wrong side of the left post.
Sadio Mane drew a straightforward save from Bernd Leno after Dani Ceballos, pressured into an error, knocked the ball straight to him in the box, before Pepe curled an effort inches wide of the top corner at the other end.
Ten minutes before the break, a VAR review preceded a Liverpool corner from which Arsenal countered and Pepe got through one-on-one – only for Adrian to block the shot.
And instead, on 41 minutes, it was Klopp’s men who found the breakthrough.
Trent Alexander-Arnold whipped in a corner from the right flank and Matip showed strength and determination to reach the ball first and plant it past Leno.
Second half
Liverpool’s objective of a quickfire second was achieved almost immediately after play restarted.
It was a simple decision for the referee to point to the spot after David Luiz prevented Salah from collecting Firmino’s clever touch with a tug of the shirt, and the Egyptian stepped up to send in an unstoppable penalty.
Aubameyang might have halved Arsenal’s deficit but, having broken the Reds’ offside trap, he allowed Matip to recover and block away his eventual hit.
And Salah punished the Gunners with a textbook goal two minutes before the hour mark.
From Fabinho’s lovely pass into the right channel, the No.11 shifted his body to leave Luiz behind, sprinted into the area on an angle and rolled a finish past the reach of Leno.
Arsenal substitute Torreira gave his side brief hope when he tucked a shot beyond Adrian with five minutes left – but Liverpool saw out the remainder to ensure they continue to set the Premier League pace.